Short answers, pulled from the story.
The term science fantasy was coined in 1935 by critic Forrest J. Ackerman, originally as a synonym for science fiction. It came into wider use after science fantasy stories appeared in American pulp magazines, and the label was most commonly applied between 1950 and 1966.
Science fiction grounds its world in natural law and presents scenarios that are scientifically plausible. Science fantasy takes supernatural or fantastical elements that could not exist under any scientific circumstances and gives them a veneer of scientific logic. Rod Serling described science fiction as "the improbable made possible" and fantasy as "the impossible made probable"; science fantasy combines both impulses.
Early science fantasy stories published in John W. Campbell Jr.'s Unknown magazine include Robert A. Heinlein's Magic, Inc., L. Ron Hubbard's Slaves of Sleep, and the Harold Shea series by Fletcher Pratt and L. Sprague de Camp. Henry Kuttner and C. L. Moore also published science fantasy novels in Startling Stories, including Moore's Northwest Smith stories.
Star Wars is debated as a science fantasy franchise. In 2015, creator George Lucas stated that "Star Wars isn't a science-fiction film, it's a fantasy film and a space opera", indicating he did not consider it science fiction.
Star Trek is sometimes classified as science fantasy because it includes supernatural and fantasy elements such as The Q alongside its science fiction setting. Writer James F. Broderick described it as science fantasy for this reason, and the late Arthur C. Clarke said he partially agreed with those who placed it in that category.
Science fantasy's freedom of imagination and romance served as an early major influence on the New Wave writers of the 1960s. Those writers grew frustrated with the constraints of hard science fiction, and the imaginative range they found in science fantasy helped shape their literary ambitions.